Machine Learning and ARIMA Model Averaging for Adaptive Public Health Forecasting: Comparative Evaluation and an Ontario COVID-19 Case Study

用于自适应公共卫生预测的机器学习与 ARIMA 模型平均：比较评估及安大略省 COVID-19 案例研究

Abstract: Public health forecasts must respond to abrupt changes in surveillance data without over-extrapolating noise, reporting artifacts, or temporary trends. We evaluated autoregressive integrated moving average (ARIMA), random forest, and extreme gradient boosting (XGBoost) models using 190 weekly observations of publicly available Ontario COVID-19 case counts from January 2020 to October 2023.

摘要： 公共卫生预测必须能够响应监测数据中的突变，同时避免对噪声、报告伪影或临时趋势进行过度推断。我们利用 2020 年 1 月至 2023 年 10 月期间安大略省公开的 190 周 COVID-19 病例数，对自回归积分滑动平均模型 (ARIMA)、随机森林 (Random Forest) 和极端梯度提升树 (XGBoost) 模型进行了评估。

Rolling-origin time-series cross-validation preserved temporal order during model tuning and evaluation. Performance was assessed across three operating dimensions: responsiveness following selected turning points, forecast horizons of one to six weeks, and the amount of historical training data. We also developed Machine Learning and ARIMA Model Averaging (MLAMA), a non-negative performance-weighted ensemble with weights that vary by forecast horizon and responsiveness setting.

在模型调优和评估过程中，我们采用了滚动原点时间序列交叉验证 (Rolling-origin time-series cross-validation) 以保持时间顺序。性能评估涵盖了三个维度：选定转折点后的响应能力、一至六周的预测范围，以及历史训练数据量。此外，我们开发了机器学习与 ARIMA 模型平均 (MLAMA) 方法，这是一种非负性能加权集成模型，其权重会根据预测范围和响应设置进行动态调整。

Retrospective comparisons showed that ARIMA adapted rapidly after turning points but its normalized error increased at longer horizons. Random forest and XGBoost were less responsive initially but maintained more stable normalized error over longer horizons. For two-week forecasts at the end of the study period, training on the most recent data outperformed using longer historical periods, particularly for XGBoost.

回顾性比较显示，ARIMA 在转折点后能迅速适应，但在较长预测周期内其归一化误差会增加。随机森林和 XGBoost 在初期响应较慢，但在较长周期内保持了更稳定的归一化误差。对于研究期末的两周预测，使用最新数据进行训练的效果优于使用较长历史周期的数据，这一点在 XGBoost 模型中尤为明显。

MLAMA achieved the lowest normalized mean absolute percentage error across most forecast horizons and ranked among the best-performing methods across responsiveness settings. These findings support selecting forecasting models according to operating conditions rather than relying on a single universally preferred approach. MLAMA provides a practical framework for combining complementary statistical and machine-learning forecasts.

MLAMA 在大多数预测周期内实现了最低的归一化平均绝对百分比误差，并在各种响应设置下均位列表现最佳的方法之列。这些研究结果支持根据具体运行条件选择预测模型，而非依赖单一的通用方法。MLAMA 为结合互补的统计学预测与机器学习预测提供了一个实用的框架。

The accompanying Python package is currently maintained in a private repository while software validation and reproducibility testing are completed.

配套的 Python 软件包目前正在私有存储库中维护，待软件验证和可重复性测试完成后发布。